Mathematics Colloquium
TOM NEEDHAM
Ohio State University
Title: Optimal Transport and Topology in Data Science
Date: Monday, January 28, 2019
Place and Time: Room 101, Love Building, 3:35-4:25 pm
Refreshments: Room 204, Love Building, 3:00 pm
Abstract. The optimal transport problem seeks the cost-minimizing plan for moving materials to building sites. It was first formulated precisely by Monge in the 1700s and has since developed into its own sophisticated subfield of pure mathematics. Recent advances in theory and algorithm design have transformed optimal transport into a viable tool for analyzing large datasets. In this talk, I will describe a way to compare general abstract metric spaces using ideas from optimal transport and demonstrate an application to feature matching of anatomical surfaces. Along the way, I will formulate several natural inverse problems in geometry and graph theory whose solutions are obtained via tools from the rapidly-developing field of topological data analysis.